Viewed just in the time domain, ordinary AM, as used in broadcasting, seems so obvious that one would scarcely imagine how it might be done otherwise. But viewed in the frequency domain, as in Chapter 6, this system shows some obvious inefficiencies. First, most of the average transmitted power (about 95% when transmitting typical audio material) is in the carrier, which is a spike or “delta function” in the frequency domain. Since its amplitude and frequency are constant, it carries virtually no information. The information is in the sidebands. Could broadcasters just suppress the carrier to reduce their electric power costs by 95%? Second, the upper and lower sidebands are mirror images of each other, so they contain the same information. Could they not suppress (filter away) one sideband, making room for twice as many stations on the AM band? The answer to both questions is yes but, in both cases, the simple AM receiver, with its envelope detector, will no longer work properly. Economics favored the simplicity of the traditional AM receiver until it because possible to put all the receiver signal processing on an integrated-circuit chip, where the additional complexity can have negligible cost. In this chapter we examine alternate AM systems that remove the carrier and then at AM systems that reduce the signal bandwidth or double the information carried in the original bandwidth.

Double-sideband suppressed-carrier AM

Let us look at a system that removes the carrier at the transmitter and regenerates it at the receiver.

In this chapter we will be mostly concerned with the sections of the receiver that come before the detector, sections that are common to nearly all receivers: AM, FM, television, cell phones, etc. Basic specifications for any kind of radio receiver are gain, dynamic range, sensitivity and selectivity, i.e., does a weak signal at the selected frequency produce a sufficiently strong and uncorrupted output (audio, video, or data) and does this output remain satisfactory in the presence of strong signals at nearby frequencies?

Sensitivity is determined by the noise power contributed by the receiver itself. Usually this is specified as an equivalent noise power at the antenna terminals. Selectivity is determined by a bandpass-limiting filter and might be specified as “3 dB down at 2 kHz from center frequency and 20 dB down at 10 kHz from center frequency.” (Receiver manufacturers usually do not specify the exact bandpass shape.)

Amplification

Let us consider how much amplification is needed in ordinary AM receivers. One milliwatt of audio power into a typical earphone produces a sound level some 100 dB above the threshold of hearing. A barely discernable audio signal can therefore be produced by −100 dBm (100 dB below 1 mW or 10–13 watts). Let us specify that a receiver, for comfortable earphone listening, must provide 50 dB more than this threshold of hearing, or 10–8 watts.

Hybrid couplers, also known as hybrid junctions or simply “hybrids,” are lossless passive four-port devices used to make interconnections between circuit elements. Hybrids are used as power dividers (“signal splitters”) and combiners. They are also used in mixers and TR (transmit/receive) switches. A useful schematic representation for a hybrid,Figure 15.1, shows the four connection points (ports).

RF hybrids usually have unbalanced ports designed for coaxial transmission lines, so all four ports share a common ground, indicated in Figure 15.1 by a dotted ground symbol (usually not shown). Each port has a characteristic impedance. Most packaged RF hybrids with coaxial ports are made so that the characteristic impedance of all four ports is 50 or 75 ohms. The symbol in Figure 15.1 shows signal flow paths; power incident on Port 1 splits and exits through Ports 2 and 3. If both of these ports are properly terminated there will be no reflections and the impedance seen looking into Port 1 will be equal to the characteristic impedance of that port. In this case no power will reach Port 4 as opposite ports are isolated. But if Port 2 and/or Port 3 are not terminated in their own characteristic impedances, the power exiting these ports will be partially or completely reflected back into the hybrid. The reflection, which depends on the mismatch, is calculated exactly as if the power had exited from a transmission line whose impedance is equal to that of the respective port.

In communications equipment, “detection” is synonymous with demodulation, the process of recovering information from the received signal. The term detector is also used for circuits designed to measure power, such as square-law microwave power detectors. In this chapter we discuss various AM, FM, and power detector circuits. The demodulator is the last module in the cascade of circuits that form a receiver and at this stage the frequencies (IF or baseband) are relatively low. For this reason the detector (and, sometimes, the final IF bandpass filter) was the first receiver section to evolve from analog to digital processing, notably in broadcast television receivers. Receivers for ordinary AM and FM have, for the most part, continued to use traditional analog detectors, but receivers for the newer digital radio formats can also use their digital signal processors to demodulate traditional AM and FM broadcasts. Demodulators for OFDM and CDMA digital modulation formats are discussed in Chapter 22.

AM detectors

There are two basic types of AM detector. An envelope detector uses rectification to produce a voltage proportional to the amplitude of the IF voltage. A “product” detector multiplies the IF signal by a reconstituted version of the carrier. This detector is a mixer (see Chapter 5), producing sum and difference frequencies. The sum component is filtered away. The difference frequency component, at f = 0 (baseband), is proportional to the amplitude of the IF voltage.

AM diode detector

The classic diode envelope detector circuit for AM is shown in Figure 18.1.

Radio astronomy was discovered accidentally in 1931 by Karl Jansky, a physicist at Bell Telephone Laboratories. Jansky had been assigned to identify the sources of noise encountered in a newly installed transatlantic short-wave radiotelephone service. Using a directional receiving antenna on 20.5 MHz, he observed that one component of the noise, a wideband hiss, had a diurnal variation that reached a maximum intensity on average four minutes earlier each day. Jansky knew that the stars advance in just this way (in siderial time) and deduced that the source of the hiss must be outside the solar system. His observations showed that this “cosmic noise” came from the galactic plane and was strongest from the direction of the galactic center (in the constellation Sagittarius).

After Jansky, the second pioneer of radio astronomy was a radio engineer, Grote Reber, who in 1937, built a 9-m (30-ft) parabolic reflector beside his house in Wheaton, Illinois. This was maybe the first modern dish antenna. Reber began his observations using a receiver at 3 GHz, which pushed the high-frequency state of the art, because he assumed that cosmic radio noise was the low-frequency tail of the thermally generated radiation spectrum from white-hot stars. The intensity of this radiation would increase as the square of the frequency, so using the highest practical frequency would make detection easier and would also make his antenna more directive.

While discussing transmitter and receiver circuitry we did not have to know much about antennas or propagation. It sufficed to know only that a voltage applied to the terminals of a transmitting antenna causes a proportional voltage to appear very shortly thereafter at the terminals of a receiving antenna. To be more exact, it was sufficient to know that everything between the terminals of the two antennas is equivalent to a linear two-port network. Here we will consider the transmission through this propagation link.

When an ac source (transmitter) is connected to an antenna (practically any metal structure) the resulting current has a component that is in phase with the applied voltage. The impedance of the antenna therefore has a real part, a resistance, and draws power from the source. If the antenna is efficient, most of the power flows away from the antenna in the form of (energy-bearing) electromagnetic waves and only a small fraction of the power will be dissipated by ohmic heating of the antenna itself. The impedance will also generally have a nonzero imaginary part, a reactance. If the reactance is zero at the operating frequency the antenna is said to be resonant, just as an RLC circuit is purely resistive at its resonant frequency. An external tuning network (an antenna tuner) can be used to cancel the reactance and also transform the resistance to a value that matches a receiver's input impedance or to a value that draws a desired amount of power from a transmitter.

In this chapter we examine how noise degrades the accuracy of digital data transmission and the fidelity of analog transmission. We begin with an explanation of matched filtering, a subject which came up in Chapter 22. We show that, for binary data links using matched filtering and coherent detection, the probability of error depends only on the noise level at the input of the receiver and on the energy, but not the shape, of the transmitted pulses. We look at two example systems: BPSK (binary phase-shift keying) with coherent detection and OOK (on–off keying) with envelope detection. The error rates and channel capacities (maximum error-free data rates when using forward error correction coding) are calculated and compared with Shannon's expression for the capacity of a band-limited channel. Finally, traditional AM and FM are examined with respect to their noise characteristics.

Matched filtering

We stated in Chapter 22 that, in the presence of noise, the post-detection signal-to-noise ratio is maximized when the predetection bandpass shape of the receiver is that of a matched filter.

A matched filter is one whose impulse response is proportional to the time-reversed waveform of the incoming signal pulse, as will be shown below. For example, if the input signal is a pulse whose shape is the same as the symmetric impulse response of a root raised-cosine filter, then the receiver should use a root raised-cosine filter or an equivalent cascade of filters.

Oscillators whose frequencies are derived from a stable reference source are used in transmitters and receivers as L.O.'s for accurate digital tuning. A VCO in a loop that tracks the frequency excursions of an incoming FM signal is a commonly used FM detector. The first widespread use of phase lock loops was in television receivers where they provide noise-resistant locking of the horizontal sweep frequency to the synchronization pulses in the signal.

Phase locking

A phase lock loop (PLL) circuit forces the phase of a voltage-controlled oscillator (VCO) to follow the phase of a reference signal. Once lock is achieved, i.e., once the phases stay close to each other, the frequency of the VCO will be equal to the frequency of the reference. In one class of applications, the PLL is used to generate a stable signal whose frequency is determined by an unstable (noisy) reference signal. Here the PLL is, in effect, a narrow bandpass filter that passes a carrier, while rejecting its noise sidebands. Examples include telemetry receivers that lock onto weak pilot signals from spacecraft and various “clock smoother” circuits. It is often necessary to lock an oscillator to the suppressed carrier of a modulated signal, an operation known as carrier recovery. In yet another class of applications the PLL is designed to detect all the phase fluctuations of the reference. An example is the PLL-based FM demodulator where the VCO reproduces the input signal, which is usually in the IF band.

In this chapter we discuss the amplifiers used commonly in the front-end and IF stages of receivers and in antenna-mounted preamplifiers. The maximum output power of these amplifiers is typically from 0.01 W to 0.1 W (10–20 dBm). The power amplifiers discussed in Chapter 3 use the full range of the transistor conductance to “push” or “pull” the output voltage to any value from zero to the dc supply voltage(s). Small-signal amplifiers, on the other hand, are class-A amplifiers in which the signal voltages are small, compared with the dc bias voltages. The small ac signals add to dc bias voltages, so the output signal, δVout, produced by an input signal δVin is given by δVout = [dVout/dVin] δVin + 1/2 [d2Vout/dVin2] (δVin)2 + ··· The ac voltage gain is, therefore, dVout/dVin, evaluated at the quiescent bias point. When operated over only a small range of δVin, the higher derivatives of Vout versus Vin make only small contributions, and the amplifier is essentially linear. Key characteristics of these amplifiers are gain, bandwidth, input and output impedances, linearity (those higher derivatives), and internally generated noise.

Linear two-port networks

Small-signal amplifiers are linear amplifiers; the output signal should be a faithful reproduction of the input signal. A general definition of small-signal amplifiers could be that they are amplifiers built entirely of nominally linear elements (which include resistors, capacitors, inductors, transmission lines, and transistors operated over a small differential range), from which it follows that the overall circuit will also be nominally linear.

A common operation in RF electronics is frequency translation, whereby all the signals in a given frequency band are shifted to a higher frequency band or to a lower frequency band. Every spectral component is shifted by the same amount. Cable television boxes, for example, shift the selected cable channel to a low VHF channel (normally channel 3 or 4). Nearly every receiver (radio, television, radar, cell phone, …) uses the superheterodyne principle, in which the desired channel is first shifted to an intermediate frequency or “IF” band. Most of the amplification and bandpass filtering is then done in the fixed IF band, with the advantage that nothing in this major portion of the receiver needs to be retuned when a different station or channel is selected. The same principle can be used in frequency-agile transmitters; it is often easier to shift an already modulated signal than to generate it from scratch at an arbitrary frequency. Frequency translation is also called conversion and is even more commonly called mixing.

Voltage multiplier as a mixer

A mixer takes the input signal or band of signals (segment of spectrum), which is to be shifted, and combines it with a reference signal whose frequency is equal to the desired shift in frequency. In a radio receiver, the reference or “L.O.” signal is a sine-wave, generated within the receiver by a local oscillator.

The S-parameter (scattering parameter) analysis technique for linear circuits has become the de facto standard in RF engineering, especially for microwave work, where it had its origins in WWII radar development. Physicists-turned-engineers, who were accustomed to analyzing the scattering (collisions) of atomic particles, used that term to describe the reflection and transmission of electromagnetic waves in electrical circuits. The resulting version of circuit theory, in terms of waves rather than currents and voltages, is convenient when working with circuits whose interconnections are transmission lines, especially when those lines are waveguides, where the definitions of voltage and current are somewhat arbitrary. The Smith chart, introduced in 1939, provided a familiar connection to the S-parameter method. In the 1960s, Hewlett Packard introduced the first network analyzers for direct S-parameter measurements.

S-parameter definitions

Keep in mind that the S parameters are just another set of transfer parameters, like the Y and Z parameters, to describe a linear circuit or circuit element at a given frequency. A two-port network is described equally well by its four complex Y parameters, its four complex Z parameters, or its four complex S parameters. Knowing one set of parameters, we can calculate any other set.

S parameter of a one-port network

A resistor, the simplest circuit element, can be described by a single parameter, its resistance, R, the ratio of voltage to current. It can be equally well described by its conductance, G, the ratio of current to voltage.